Discovery of the massive overcontact binary VFTS 352: Evidence

for enhanced internal mixing

L.A. Almeida1,2,3, H. Sana4,5, S.E. de Mink6, F. Tramper6, I. Soszynski7, N. Langer8, R.H.

Barba9, M. Cantiello10 A. Damineli2, A. de Koter6,11, M. Garcia12, G. Grafener16, A.

Herrero13,14, I. Howarth15, J. Maız Apellaniz12, C. Norman1, O.H. Ramırez-Agudelo6, J.S.

Vink16

ABSTRACT

The contact phase expected to precede the coalescence of two massive stars

is poorly characterized due to the paucity of observational constraints. Here

1Department of Physics & Astronomy, Johns Hopkins University, Bloomberg Center for Physics and

Astronomy, Room 520, 3400 N Charles St

2Instituto de Astronomia, Geofısica e Ciencias, Rua do Matao 1226, Cidade Universitaria Sao Paulo, SP,

Brasil, 05508-090

3Email: leonadodealmeida.andrade@gmail.com

4European Space Agency/Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD

21218, United States

5Institute of Astronomy, KU Leuven, Celestijnlaan 200D, 3001 Leuven, Belgium

6Anton Pannenkoek Astronomical Institute, University of Amsterdam, 1090 GE Amsterdam, The Nether-

lands

7Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warszawa, Poland

8Argelander-Institut fr Astronomie, der Universitat Bonn, Auf dem Hgel 71, 53121 Bonn, Germany

9Departamento de Fısica y Astronomıa, Universidad de La Serena, Av. Cisternas 1200 Norte, La Serena,

Chile

10Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA

11Instituut voor Sterrenkunde, Universiteit Leuven, Celestijnenlaan 200 D, 3001, Leuven, Belgium

12Departamento de Astrofısica, Centro de Astrobiologıa (INTA-CSIC), campus ESA, apartado postal 78,

28 691 Villanueva de la Canada, Madrid, Spain

13Instituto de Astrofısica de Canarias, C/ Vıa Lactea s/n, E-38200 La Laguna, Tenerife, Spain

14Departamento de Astrofısica, Universidad de La Laguna, Avda. Astrofısico Francisco Sanchez s/n,

E-38071 La Laguna, Tenerife, Spain

15Department Physics & Astronomy, University College London, Gower Street, London WC1E 6BT, UK

16Armagh Observatory, College Hill, Armagh, BT61 9DG, Northern Ireland, UK

arX

iv:1

509.

0894

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[as

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ph.S

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Sep

2015

– 2 –

we report on the discovery of VFTS 352, an O-type binary in the 30 Do-

radus region, as the most massive and earliest spectral type overcontact system

known to date. We derived the 3D geometry of the system, its orbital period

Porb = 1.1241452(4) d, components’ effective temperatures – T1 = 42 540±280 K

and T2 = 41 120 ± 290 K – and dynamical masses – M1 = 28.63 ± 0.30 Mand M2 = 28.85 ± 0.30 M. Compared to single-star evolutionary models, the

VFTS 352 components are too hot for their dynamical masses by about 2700 and

1100 K, respectively. These results can be explained naturally as a result of en-

hanced mixing, theoretically predicted to occur in very short-period tidally-locked

systems. The VFTS 352 components are two of the best candidates identified so

far to undergo this so-called chemically homogeneous evolution. The future of

VFTS 352 is uncertain. If the two stars merge, a very rapidly rotating star will

be produced. Instead, if the stars continue to evolve homogeneously and keep

shrinking within their Roche Lobes, coalescence can be avoided. In this case,

tides may counteract the spin down by winds such that the VFTS 352 compo-

nents may, at the end of their life, fulfill the requirements for long gamma-ray

burst (GRB) progenitors in the collapsar scenario. Independently of whether the

VFTS 352 components become GRB progenitors, this scenario makes VFTS 352

interesting as a progenitor of a black hole binary, hence as a potential gravita-

tional wave source through black hole-black hole merger.

Subject headings: stars: early-type — stars: massive — binaries: spectroscopic

— binaries: eclipsing — binaries: close — stars: individual: VFTS 352

1. INTRODUCTION

Massive stars are one of the most important cosmic engines driving the evolution of

galaxies throughout the history of the universe. In the Milky Way, most massive stars

are born as part of a binary system with an orbital period Porb < 4 yr (Mason et al.

2009; Sana et al. 2012), i.e. close enough to interact during their lifetime through mass-

exchange or coalescence (Podsiadlowski et al. 1992). Such binary interactions have important

consequences for the subsequent evolution of the components of the system and lead to key

astrophysical phenomena such as double compact binaries, hydrogen-deficient core-collapse

supernovae and gamma-ray bursts (GRBs). The high frequency of close binaries further

challenges the accepted predominance of the single-star evolutionary channel.

Binary interaction may happen early in the evolution of the stars. According to the

massive star multiplicity properties derived from galactic young open clusters (Sana et al.

– 3 –

2012), 40% of all O-type stars may interact with a nearby companion before leaving the

main sequence and over half these main sequence interactions (about a quarter of all stars

born as O type) will lead to a deep contact phase of which the most likely outcome will be

coalescence. Such a process modifies the mass function of massive star clusters, and may

help to create some of the most massive stars known (Crowther et al. 2010; Schneider et al.

2014).

Despite possibly affecting almost one quarter of all O-type stars, the deep contact phase

is one of the least understood phases of massive binary evolution. This results from the

complex interplay between a variety of physical processes, including mass exchange, tidal

locking, intense mutual illumination, internal mixing, angular momentum loss, as well as

possible adjustments to the stars internal structure (Pols 1994; Wellstein et al. 2001; de

Mink et al. 2007).

Our limited understanding also stems from the almost complete absence of observational

constraints. Observationally, these interacting binaries are expected to reveal themselves as

overcontact binaries, i.e. an orbital configuration in which both components are overfilling

their Roche lobes (Wilson 2001). However, only three O-type overcontact binaries are known

to date (see Sect. 4.1).

Located in the Tarantula Nebula (30 Dor, Fig. 1) in the Large Magellanic Cloud (LMC),

VFTS 352 is a double-lined spectroscopic binary identified by the VLT-FLAMES Tarantula

Survey (VFTS, Evans et al. 2011; Sana et al. 2013). Classified as O4.5 V(n)((fc))z + O5.5

V(n)((fc))z (Walborn et al. 2014), both companions present rotationally broadened H I, He I

and He II absorption lines. In this study we present the results of the analysis of an 18-

month spectroscopic monitoring of VFTS 352 combined with ∼12 years of OGLE-III and IV

photometry (Udalski et al. 2008).

2. OBSERVATIONS AND DATA REDUCTION

2.1. Spectroscopy

New spectroscopic data of VFTS 352 were collected as part of the Tarantula Massive

Binary Monitoring program (PI: Sana) at the ESO Very Large Telescope (VLT). 32 spectro-

scopic epochs were obtained from October 2012 to March 2014 using the FLAMES-GIRAFFE

multi-object spectrograph and the LR02 grism, providing continuous coverage of the 3950–

4550 A region with a spectral resolving power λ/∆λ of 6,400. Three sets of back-to-back

exposures were taken to ensure optimal cosmic-ray removal. The six LR02 spectra obtained

as part of the VFTS were further included in our analysis.

– 4 –

5.605.615.625.635.645.655.665.675.68

Right Ascension (hour)

−69.30

−69.25

−69.20

−69.15

−69.10

−69.05

−69.00

−68.95

−68.90

Declin

ation (

degre

e)

O starsVFTS 352

Fig. 1.— Location of VFTS 352 in the 30 Dor field-of-view. All O-type stars observed by the

VFTS are also marked. The two circles indicate the locations of NGC2070 (at the center)

and NGC 2060 (to the South-West).

– 5 –

The data reduction was performed using the ESO CPL GIRAFFE pipeline v.2.12.1. It

involved the standard steps of bias subtraction, flat-field structure removal, extraction, and

wavelength calibration. Additional steps of sky correction and normalization were applied

following the procedures described in Evans et al. (2011) and Sana et al. (2013), respectively.

Figure 2 shows examples of normalized individual spectra.

2.2. Photometry

V− and I−band time-resolved photometry were obtained by the OGLE-III and IV

projects (Udalski et al. 2008). The temporal coverage of the OGLE-III and IV data is of

∼7.5 and 5.2 years, respectively, with an accuracy of a few mmag. There is a small shift

(∼0.01 mag) in brightness between OGLE-III and OGLE-IV light curves due to independent

calibration which has an accurancy of about 0.02 mag (Udalski et al. 2008). The total

number of VFTS 352 measurements available in the V− and I−bands is 90 and 760. Both

light curves show ellipsoidal variations with semi-amplitude of ∼ 0.1 mag indicating that at

least one component of the system is filling its Roche lobe or is close to doing so.

3. ANALYSIS AND RESULTS

3.1. Radial velocity measurements

The radial velocities of the VFTS 352 components were obtained following the procedure

described in Sana et al. (2013). In brief, we simultaneously adjusted the He I λλ4388, 4471

and He II λλ4200, 4541 lines at all epochs using Gaussian profiles. The shape of the Gaussian

profile for each spectral line and each component is kept constant at all epochs, allowing for

enhanced robustness of the fitting at phases where the lines are heavily blended or where

the S/N is poorer. The obtained RVs and 1σ error bars are available at the Centre de

Donnees astronomiques de Strasbourg1 (CDS) together with the journal of the observations.

The best-fit RV-only orbital solution yields semi-amplitudes of K1 = 324.9± 5.8 km s−1 and

K2 = 315.6±6.2 km s−1 for the primary and secondary components. In the next section, the

RV-only solution that we obtain is used as a starting point for the combined photometric

and spectroscopic orbital solution.

1http://vizier.u-strasbg.fr/

– 6 –

3.2. Simultaneous modeling of light curves and radial velocities

To obtain the geometrical and physical parameters of VFTS 352, we simultaneously

adjusted synthetic light and radial velocity curves generated by the Wilson Devinney code

(WDC, Wilson & Devinney 1971) to the V− and I−band OGLE-IV light curves and the

VLT/FLAMES radial velocity curves. We follow the procedure presented in Almeida et al.

(2012) to search for the global solution. In essence, the WDC is used as a function to be

optimized by the genetic algorithm PIKAIA (Charbonneau 1995) followed by a Markov chain

Monte Carlo (MCMC) procedure (Gilks, Richardson & Spiegelhalter 1996) to sample the

parameters and obtain their uncertainties.

To restrict the size of the explored parameter space, we use priors obtained from our

initial radial velocity solution (Sect. 3.1) and from the known spectral type of the components

(Walborn et al. 2014). We constrain the mass ratio (q = M2/M1) between 0.95 < q < 1.05,

and effective temperatures, 40900 < Teff,1 < 44900 and 38900 K < Teff,2 < 42900 K, with

42900 and 40900 K (Walborn et al. 2014) as a starting point for the primary and secondary

respectively. We also keep fixed the distance d = 50 kpc and the V−band extinction Av =

1.109± 0046 (Maız Apellaniz et al. 2014). As the light curves show ellipsoidal variation and

q ∼ 1, we try to model the data with overcontact, contact, and semi-detached configurations,

but only the overcontact model provides a plausible solution (see the top panel of Figure 3).

In all these models, non-Keplerian effects (tidal distortion of the stars) are taken into account.

To account for the temperature difference between the components (see Section 3.3), we

use the mode 3 of the WDC which has no constrain in the temperature, bolometric albedo,

gravity brightening, and limb darkening coefficients of the secondary star. WDC converts

the mean surface effective temperatures, T1 and T2, in polar temperature using Eq. 8 of

Wilson (1979) and then computes the local temperature using gravity brightening law and

polar temperature. The linear limb darkening coefficients were computed for both stars as a

function of Teff and log g. In this purpose, the coefficients calculated by Dıaz-Cordoves et al.

(1995) and Claret et al. (1995) are automatically updated while the program is running. The

best solution for VFTS 352 is shown in Figure 3 and the adjusted and derived parameters

are listed in Table 1.

3.3. Atmosphere analysis

We employ the line-blanketed non-local thermodynamic equilibrium atmosphere code

fastwind (Puls et al. 2005) to model both components of VFTS 352. For our initial models

we use the values for the radius, gravity and temperatures listed in Table 1 as input. We

– 7 –

Table 1: Best fit parameters resulting from the simultaneous adjustment in the I− and V−band light curves and radial velocity curves of the components.

Parameter Value

Adjusted Parameters

Porb (d) 1.1241452 ± 0.0000004

T0 (HJD) 2455261.119 ± 0.003

q = M2/M1 1.010 ± 0.010

Ωa1 3.584 ± 0.014

Ωa2 3.584 ± 0.014

T1 (K) 42540 ± 280

T2 (K) 41120 ± 290

i () 55.60 ± 0.20

ab (R) 17.55 ± 0.06

γ (km s−1) 262.8 ± 1.2

Roche radii

Rpole1 /RL 1.005 ± 0.001

Rside1 /RL 1.070 ± 0.001

Rback1 /RL 1.192 ± 0.001

Rmean1 /RL 1.089 ± 0.001

Rpole2 /RL 1.004 ± 0.001

Rside2 /RL 1.067 ± 0.001

Rback2 /RL 1.189 ± 0.001

Rmean2 /RL 1.087 ± 0.001

Derived parameters

M1 (M) 28.63 ± 0.30

M2 (M) 28.85 ± 0.30

Rmean1 (R) 7.22 ± 0.02

Rmean2 (R) 7.25 ± 0.02

log g1 [cm s−2] 4.18 ± 0.01

log g2 [cm s−2] 4.18 ± 0.01

Mbol1 −8.26 ± 0.01

Mbol2 −8.08 ± 0.01

a Roche surface potential - Ω2 = Ω1 in mode 3 of the WDC;b Binary separation.

– 8 –

adopt the Vink et al. (2001) mass-loss rates based on the stellar parameters and an LMC

metallicity and we use the scaling with the escape velocity (vesc) to estimate the wind ter-

minal velocity (v∞ = 2.65 × vesc; Kudritzki & Puls 2000). Finally, we adopt rotation rates

corresponding to a fully synchronized system, i.e. vrot = 325 km s−1, and we use the orbital

inclination value (i) from Table 1 to compute the projected rotation velocity at the equator.

The model that we obtained (Figure 2) further takes into account the phase dependance

of the brightness ratio of the two components and provides a satisfactory representation of

the data. In addition to the physical parameters, we also investigate the helium surface

abundance in the VFTS 352 spectra. While we could not find any clear signature of enrich-

ment, we estimate that a surface enrichment corresponding to a mass fraction XHe less than

40% would be hard to detect with our data.

Figure 2 also reveals small variations in the intensity of the He I lines. Such a behaviour

is reminiscent of the Struve-Shade effect (Bagnuolo et al. 1999; Linder et al. 2007) and

possibly results from temperature structure on the (deformed) stellar surface (Palate &

Rauw 2012). Future spectral disentangling, taking into account the phase dependance flux-

ratio of the object – may help to lower the present upper limit on the He surface abundance.

Combined with phase-resolved spectral modelling, it would further help to elucidate the

nature of the He I lines line profile variability. These two aspects however lay beyond the

scope of the present work.

3.4. Orbital period variation

To search for indication of variations in the orbital configuration of VFTS 352, we scruti-

nize its orbital period. We split the OGLE-III and IV I−band photometric data – which span

12.5 years – into 15 parts that we analyze separately using the WDC. As all the VFTS 352

parameters are well determined (see Table 1), we allow them to vary only within ±1 σ from

their best-fit value and we leave the orbital period as the only entirely free parameter. The

MCMC procedure was used to sample the posterior distribution of the orbital period and

obtain the best value as well as its uncertainty.

With a peak-to-peak variation of ∼2 s over a 12.5 yr time span, the variation time scale

of the VFTS 352 orbital period is approximately P/P ≈ 0.6 Myr, see Fig. 4. Such a relatively

long time scale suggests that the system may currenty be stable, thus the overcontact config-

uration relatively long lived. In that case, the relevant evolutionary time scale for the system

is the nuclear time scale. The apparent stability of the VFTS 352 configuration would then

favour an evolutionary stage that corresponds to the rather long-lasting overcontact phase

– 9 –

predicted by Case A mass transfer scenarios (Pols 1994; Wellstein et al. 2001).

4. DISCUSSION AND CONCLUSION

4.1. Physical properties

The simultaneous analysis of the RV and light curves of VFTS 352 indicates that this

system is in an overcontact configuration. While a number of massive contact binaries are

known, i.e. systems where both stars just fill their Roche lobes (e.g. MY Cam and UW CMa,

Lorenzo et al. 2014; Leung & Schneider 1978; Antokhina et al. 2011) only a few overcontact

O-type systems have been identified so far: TU Mus (O8 V(n)z + B0 V(n); Porb = 1.38 d,

Penny et al. 2008; Sota et al. 2014) and V382 Cyg (O7 V + O7 V; Porb = 1.89 d, Popper

1978; Degirmenci et al. 1999) in the Milky Way, and OGLE SMC-SC10 108086 (O7 V +

O8 V; Porb = 0.88 d, Hilditch et al. 2005) in the Small Magellanic Cloud.

By comparing the stars’ volumes with those of their Roche lobes, one can estimate the

degree of (over)contact. For this purpose, we define the Roche volume (over)filling factor

fL as the ratio between the volume of the star and that of its Roche lobe. fL can be

approximated as

fL =

(Rmean

RL

)3

, (1)

with Rmean, the average stellar radius and RL, the effective Roche lobe radius that we com-

pute using Eggleton (1983) approximation. According to this definition, both components of

VFTS 352 have fL ≈ 1.29. Stars in TU Mus have fL ≈ 1.30 and 1.24 while the components

of V382 Cyg and OGLE SMC-SC10 108086 have fL ≈ 1.1 and 1.7, respectively.

According to their spectral classifications, the VFTS 352 primary and secondary com-

ponents have effective temperatures of about 42 900 K and 40 900 K (Walborn et al. 2014).

These values agree very well with the results of the light curves fitting – T1 = 42540± 280 K

and T2 = 41120± 290 K – and are further consistent with the observed spectra of VFTS 352

(Sect. 3.3). The good agreement between the three methods suggests robust effective tem-

perature estimates.

Figure 5 compares the location of the VFTS 352 components in the Hertzsprung-Russell

diagram (HRD) with those of the other known overcontact binaries. It reveals that VFTS 352

is the earliest-type, hottest and most massive overcontact binary known to date. VFTS 352

is also the second shortest orbital period system and the only one with a mass-ratio close to

unity.

– 10 –

At 1 Myr, single stars of 28.63 and 28.85 M with initial spin rates ≈ 330 km s−1

are expected to have effective temperatures of 39 880 and 39 980 K (Brott et al. 2011).

The VFTS 352 components are thus hotter by about 2700 and 1100 K, respectively. As

a confirmation, Fig. 6 shows that the quasi-absence of He I λλ4143, 4387 and the weak

He I λ4471 in the primary spectrum cannot be reconciled with the temperature of 39 880 K

that is expected given its mass, its spin rate and the Brott et al. models. To be noted, the

fastwind models in Figs. 2 and 6 are not fitted but serve as a check that the light curve

fitting result and, in particular, its absolute temperature scale, are fully consistent with the

object spectrum. Interestingly, the primary is the most luminous and hottest component of

the system, but it is also the less massive one. This is a clear indication that the primary

has a larger helium content, thus that it is more evolved, than the secondary.

4.2. Evolutionary status

Our photometric and spectroscopic solution shows that the system has a mass-ratio very

close to unity. Twin binaries are expected to be common among high-mass systems with

short orbital period (Krumholz & Thompson 2007). This results from the fact that mass

transfer takes place very early in their life. In such case, the mass transfer starts with a fast

Case A, occurring on the thermal timescale of the components, until the system reaches a

mass-ratio close to one. At that point, it switches to a slow Case A, which develops itself on

the nuclear timescale (Kippenhahn & Weigert 1967). Given the relative timescales involved,

it is more probable that we are observing VFTS 352 during its slow Case A phase, as already

suggesed in Sect. 3.4.

There are currently no models for massive stars reliably predicting the physical prop-

erties of the stars during the overcontact phase. Even though the models by de Mink et al.

(2007) computed with the TWIN version of the Eggleton code (Eggleton 2006) allow for the

formation of (shallow) contact, they do not include a realistic treatment of heat transfer dur-

ing the contact phase. For low mass contact binaries this appears to be a crucial ingredient

(Yakut & Eggleton 2005). At today’s day, our results can thus not be directly confronted

with theoretical binary computations. In an attempt to identify physical processes that are

specific to the present configuration, we instead looked for deviations between the properties

of VFTS 352 and the predictions of single stellar models.

To obtain a precise interpolation of the single star evolutionary tracks of Brott et al.

(2011), we use the Bayesian comparison tool BONNSAI2 (Schneider et al. 2014). We adopt

2The BONNSAI web-service is available at www.astro.uni-bonn.de/stars/bonnsai.

– 11 –

a Salpeter initial mass function and a flat rotational distribution as priors and we provide

the temperatures, masses, luminosities and rotation rates that we measured. As can be seen

in Fig. 5 (lefthand panel), no model can self-consistently reproduce all the observables at

once: the stars appear too hot for their dynamical masses.

Comparing the Bonn’s evolutionary tracks with binary results listed in the review of

Torres et al. (2010), Schneider et al. (2014) also found that systems with effective tem-

peratures higher than 25000 K tend to be hotter than expected for their dynamical mass,

although the difference was of the order of 1000 K only. While this could indicate a sys-

tematic discrepancy between observed and modelled effective temperatures, Schneider et al.

(2014) also suggested that the difference could be due to calibration issues.

In particular, we reviewed the only four O-type binaries listed in Torres et al. (2010)

and found that, in the original analysis of these systems, the authors used the primary

temperature fixed from its spectral type. While this is a logical approach if the distance

is a free parameter, it is susceptible to significant bias if a problem occurs in the adopted

calibrations. Furthermore, the error will propagate to the secondary star properties as well.

Indeed, the calibrations adopted in the original analyses were outdated, e.g., Lamers (1981),

Popper (1980), Conti (1973), Conti (1973), etc. They carry a systematic shift to higher

temperatures (∼ 1000 K) compared to more recent models which take into account non-

LTE, wind, and line-blanketing effects, e.g., Martins et al. (2005). For example, the V3903

Sgr system was analyzed by Vaz et al. (1997). They used Conti (1973) and Lamers (1981) to

fixed the primary effective temperature T1 =38000 K, for an O7V spectral type. However,

an O7V has 36872 K in Martins et al. (2005), therefore, ∼1100 K lower.

According to this discussion, one would need to re-analyze all hot systems listed in Torres

et al. (2010) using modern state-of-the-art calibration and sophisticated models. While this

would be an important work, it lays far beyond the present paper. We however emphasis

that, in the VFTS 352 analysis, we do not use a fixed primary temperature but adjusted

both T1 and T2, see Section 3.2. As a consequence, our analysis does not suffer from the

same drawback as the historical analyses quoted by Torres et al. (2010).

Interestingly, we find that rapidly rotating single star models can reproduce the masses,

luminosities and temperatures of the VFTS 352 components. A good match is found adopting

initial rotation rates of 450+70−10 km s−1 (Fig. 5, right hand panel). Such high rotation rates

are of course ruled out by the widths of the spectral lines in the VLT/FLAMES data and

would further not be expected given tidal locking. However, the good agreement between

these extreme rotating models and the observed stellar parameters may be interpreted as

evidence that the VFTS 352 components have experienced more mixing than comparable

single stars, possibly as a result of their binary nature.

– 12 –

4.3. Signature of enhanced mixing?

As mentioned in the previous section, the best fitting single star models are those that

experienced enhanced internal mixing. The high temperatures and compactness of VFTS 352

can indeed be explained if extra helium produced in the center of the star is mixed throughout

the envelope resulting in quasi homogeneous stars (Maeder 1987; Yoon & Langer 2005).

For the single star models of Brott et al. (2011) that we used above, enhanced mixing is

a consequence of rotationally induced instabilities. While the single star models are not

appropriate for direct comparison, the good match between these fast rotating models and

the physical properties of the VFTS 352 components may be a signature that the stars have

experienced additional mixing compared to similar single star with a 330 km s−1 rotation

rate, even if the nature of the additional mixing processes in VFTS 352 may differ from those

implemented in single star models.

Stars in close binary systems are generally thought to experience enhanced mixing in

comparison with a single stellar models with the same birth rotation rate (e.g., de Mink et

al. 2009; Song et al. 2013). For example, (1) tidal locking of the rotation period of the outer

stellar layers with the orbital period creates internal shear. The shear can persist as the

star evolves and its internal structure slowly changes. As the tides force the stars to stay

in synchronous, (2) angular momentum from the orbit is converted into the spin angular

momentum of the stars. For single stellar models higher angular momentum implies more

internal mixing. If this holds true for binary systems, it would imply enhanced mixing.

Finally, (3) the deformation of stars that are very close to filling their roche lobe may also

play a role. In single stars the deviation of spherical symmetry is the seed for the Von Zeipel

effect and the Eddington-Sweet circulations. For close binary stars the symmetry around

the rotation axis is also broken, adding further possibilities for internal processes to enhance

mixing.

It is unclear how these processes (and possible additional processes not listerd here)

operate and possibly interplay with each other. Attempts to account for (some of) this

additional physics were made by de Mink et al. (2009) and later independently by Song

et al. (2013). Both groups indeed predict that stars in compact binaries experience more

mixing than single stars with identical birth rotation rate. This is consistent with our finding

that the best matching single star models have higher initial rotation rates than expected

for VFTS 352.

The models by de Mink et al. (2009) further predict enhancements of the surface with

CNO burning products. The rapidly rotating single star models that reproduce our obser-

vations imply a surface helium mass fraction of 39 and 32% for the primary and secondary

components. These indirectly inferred abundances are consistent with the detection limits

– 13 –

obtained from our spectra.

4.4. Alternative scenarios without enhanced mixing

An alternative explanation for the high temperatures and increased helium surface abun-

dance that does not invoke enhanced mixing involves stripping of a star from its enveloppe.

This exposes the deeper layers which show signatures of the nuclear burning in the center

of the convective core. In absence of extra mixing one needs to strip the star(s) down to

the layers that were once part of the convective core. The removal of a star’s outer layers

can be achieved either through stellar winds or by Roche lobe overflow and subsequent mass

transfer. Here we briefly discuss these scenarios.

While stellar winds can play a major role in the advanced evolutionary stages of massive

stars, we expect them to have had a negligible effect for the relatively unevolved components

of VFTS 352. There are no significant wind spectral signatures in the spectrum of VFTS 352

(Walborn et al. 2014). The reduced metallicity of the LMC also implies that the role of

stellar winds in this early stage is neglible. We thus conclude that stripping by stellar winds

alone is unable to remove a substantial part of the envelope.

The second scenario concerns Roche lobe overflow by the initially most massive star and

(partial) accretion by the companion. Allthough some mass loss due to Roche lobe overflow

seems likely, it is hard – within our current understanding of binary interaction – to reconcile

the VFTS 352 observables using mass transfer alone (i.e. without invoking extra mixing). To

explain the surface helium enrichment of the primary star – 39% by mass – in absence of

extra mixing, the star needs to shed about half of its total mass. This implies an extreme

initial mass ratio M2/M1 ∼< 0.5, with the exact value depending on how much the mass gainer

accreted. Mass transfer in systems with such extreme mass ratios is expected to be highly

non-conservative due to the thermal expansion of the mass gainer (Pols 1994; Wellstein et

al. 2001; de Mink et al. 2007). Also the current short orbital period of VFTS 352 may be

seen as an indication of a prior non-conservative evolution that has resulted in a shrinkage

of an originally wider orbit.

Yet, this picture is very hard to reconcile with the inferred helium surface enrichment

of the secondary – 32% by mass fraction – which suggests that the secondary has accreted

at least some of the primary enriched material. A simple back-of the enveloppe calculation

indeed shows that, assuming a primary enriched material with a 39% He-mass fraction at

most, the secondary star should have accreted at least 6 M in order to increase the He-mass

fraction of its enveloppe from 26% to 32%. This contradicts the non-conservative nature of

– 14 –

the scenario implied by the very low initial mass-ratio and current short orbital period.

Reversing the role of the primary and secondary in this scenario does not help, hence mass

transfer alone is unable to provide a satisfactory explanation either.

In view of the current state of the models, it seems that neither stellar winds nor

Roche lobe overflow, acting alone, are sufficient mechanisms to provide a simple and natural

explanation for the inferred properties of VFTS 352. We thus suggest enhanced internal

mixing, either as the sole culprit or in combination with the processes above, as the most

probable explanation for their current properties.

4.5. Age constraints

If the VFTS 352 components are evolving quasi-homogeneously under the combined

effects of rotation and tidally-induced enhanced mixing, the position of the stars in the HRD

would then remain close to the zero-age main sequence for the first few Myr of their life

(Brott et al. 2011). Given our constraints on the temperature and luminosities, we obtain

age estimates of 3.4±0.2 and 2.4±0.2 Myr for the primary and the secondary. Both the higher

helium mass fraction of the primary and the different age estimates provide indications of a

previous mass-transfer event.

The age that we infer opens up to the possibility that the system was not born at its

current location but may have migrated from one of the young 30 Doradus clusters after

receiving an impulse through dynamical interaction (e.g. Fujii & Portegies Zwart 2011). The

systemic radial velocity, γ = 262.8 ± 1.2 km s−1, is in overall agreement with that of the

30 Doradus region and does not indicate that the system is a runaway star along the line

of sight. We inspected the OGLE data and, while the dispersion of the measurements is

large, a significant proper motion of the order of −0.8± 0.3 milli-arcsec yr−1 may be present

along the declination axis. While error bars are large, such a proper motion allows for the

possibility that the system has been ejected from the NGC 2070 association or from R136,

the very massive cluster at its core. An ongoing HST proper motion program (GO 13359,

PI: Lennon) will soon be able to confirm the tentative proper-motion detected in the OGLE

data.

4.6. Final fate

Two possible outcomes of the overcontact configuration of VFTS 352 can be envisioned,

depending on whether the stars will evolve redward or blueward in the HRD. In the first

– 15 –

scenario, the build-up of an internal chemical gradient will reduce the efficiency of the

rotationally- and (possibly) tidally-induced mixing over time. Stars will then switch to

a more standard evolution scenario in which secular expansion will push the VFTS 352 com-

ponents into deeper contact and the system will eventually merge.

While the merging process itself is poorly understood, it may produce an intermediate

luminosity transient (Soker & Tylenda 2006), such as the one associated with the merger of

the lower-mass system V1309 Sco (Tylenda et al. 2011). The likely outcome of the merging

process is a rapidly rotating and possibly magnetic single star (Ferrario et al. 2009; Langer

2012; de Mink et al. 2013, 2014). According to the models by Yoon et al. (2006) and Brott et

al. (2011), such a fast rotating massive star may itself experience significant mixing induced

by rotation. A similar system at low metallicity might even retain enough angular momentum

to fulfill the requirements of the collapsar scenario (Woosley 1993) for the progenitors of long

GRBs as suggested by Yoon & Langer (2005) and Woosley & Heger (2006).

In the second scenario, the internal mixing is such that the stars would pursue (quasi)

chemically homogeneous evolution. They would become hotter and more luminous, but

would remain compact. The system may thus avoid the coalescence phase described above

and the stars would retain their tidally-locked rapid rotation rate throughout their main

sequence lifetime (de Mink et al. 2009). Once most of the stellar hydrogen will have been

burned, the VFTS 352 components are then expected to enter a Wolf-Rayet phase and to

develop strong stellar winds.

Tides can in principle counteract the spin down induced by mass-loss and preserve the

rapid rotation. This however depends on uncertain aspects such as how much the orbit

widens during this phase and how efficient the tides are. If the components in VFTS 352

can retain their high spins until the end of their lives they would be interesting candidates as

progenitors of long Gamma-ray bursts, despite the relatively high-metallicity environment

provided by the LMC.

Regardless of the evolution of the stellar spin, a scenario in which VFTS 352 avoids

coalescence implies two massive stars whose cores are enlarged as a result of mixing. In such

a configuration, the most likely final outcome of is the formation of two stellar mass black

holes. This makes VFTS 352 also interesting as a potential progenitor of binary black hole

merger and gravitational wave source.

– 16 –

ACKNOWLEDGMENTS

This work is based on data obtained at the European Southern Observatory under

program IDs. 182.D-0222, 090.D-0323, and 092.D-0136. The authors are grateful to the

referee for comments that help improving the manuscript, to N.R. Walborn for fruitful

discussions and to J. Pritchard and the ESO staff for their support during the observing

campaigns. LAA acknowledges support from the Fundacao de Amparo a Pesquisa do Estado

de Sao Paulo - FAPESP (2013/18245-0 and 2012/09716-6); SdM, from a Marie Sklodowska-

Curie Reintegration Fellowship (H2020-MSCA-IF-2014, project id 661502) awarded by the

European Commission; J.M.A., from the Spanish Government through grant AYA2013-

40 611-P; R.H.B., from FONDECYT No 1140076. This work has been partly supported by

the Polish National Science Centre grant No. DEC-2011/03/B/ST9/02573.

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This preprint was prepared with the AAS LATEX macros v5.2.

– 20 –

4000 4100 4200 4300 4400 4500Wavelength (

A)

0.6

0.8

1.0

1.2

1.4

1.6

Nor

mal

ized

Flu

x

Hε

He

I+II

4026

Hδ

He

II 42

00

Hγ

He

I 447

1

He

II 45

41

φ=0.698

φ=0.528

φ=0.139

Fig. 2.— Examples of VFTS 352 spectra at three different epochs illustrating the Doppler

shift of the H I, He I, and He II lines. Overplotted are the fastwind models described in

Section 3.3 for primary (blue lines), secondary (red lines), and the combination of both com-

ponents (green lines). The combined line profiles reproduce the observed binary spectrum

very well.

– 21 –

Φ = 0.00Φ = 0.125

Φ = 0.25

Φ = 0.375Φ = 0.50

Φ = 0.675

Φ = 0.75

Φ = 0.875

Fig. 3.— From the top to the bottom panels are: snapshots of VFTS 352 at few orbital

phases, as viewed from an orbital inclination angle i of 55.6 deg; and best WDC model

simultaneously fitted to the V− and I− band light curves and radial velocity curves, respec-

tively.

– 22 –

Fig. 4.— Orbital period variation of VFTS 352. The orbital period measurements obtained

from OGLE-III and IV I−band photometric data are shown as filled and open circles re-

spectively.

– 23 –

Fig. 5.— Location of the VFTS 352 components on the H-R diagram. Single-star evolution-

ary tracks (solid lines) and isochrones (dashed lines) of Brott et al. (2011) are overlaid and

correspond to initial rotation rates of 330 and 440 km s−1 for the left- and right-hand side

panels, respectively. The positions of the Galactic (TU Mus, V382 Cyg) and SMC (OGLE

SMC-SC10 108086; #10) contact binaries are indicated for comparison.

Fig. 6.— Close up on H I, He I and He II line profiles in the spectrum of VFTS 352

(φ = 0.139) compared to fastwind models computed with the best fit parameters of Table 1

(plain green line) and with a ± 2700 K difference in the primary effective temperature T1

(blue and red dashed lines). While the green curve seems to fit the HeIλλ4026 better than

the red curve, this helium line is a trace element in such a hot star and strongly impacted

by the Struve Struve-Sahade effect as discussed in Section 3.3.